Handout
Wolfram Research

Wolfram Math World: Hyperboloid

For Students 9th - 10th
This Math World site explains how the hyperboloid is created from a hyperbola, illustrated with graphs. The site then goes into detail giving the parametric and cartesian equations for a one sheeted hyperboloid and then the two sheeted...
Activity
University of St. Andrews (UK)

University of St. Andrews: Hyperbola

For Students 9th - 10th Standards
This University of St. Andrews site gives the parametric and cartesian equation for a hyperbola along with an example graph. The site offers links to related curves.
Activity
Varsity Tutors

Varsity Tutors: Hotmath: Practice Problems: Conic Sections

For Students 9th - 10th Standards
Hotmath provides 26 practice problems relating to conic sections. Each of the practice problems include a step-by-step guide for solving their conic.
Website
Other

College of the Redwoods: Conchoid Nicomedes

For Students 9th - 10th Standards
This resource derives the equations and gives several examples of Conchoid Nicomedes.
Graphic
University of St. Andrews (UK)

University of St. Andrews: Involute of a Circle

For Students 9th - 10th
This site from the University of Saint Andrews shows the involute of a circle graphically and gives brief history. Cartesian equation is given.
Activity
Texas Instruments

Texas Instruments: Numb3 Rs: Cycloid I

For Teachers 9th - 10th
Based off of the hit television show NUMB3RS, this lesson is more about student prediction and reasoning than actual formal math. In the lesson, students are to propose the shape that would be formed by a point on a bicycle tire, while...
Graphic
Interactive Mathematics

Interactive Mathematics: Lissajous Figures

For Students 9th - 10th
Students examine a special case of parametric equations called Lissajous figures. Definitions, graphs, and detailed examples are included.
Graphic
Other

Personal: Astroid

For Students 9th - 10th Standards
Excellent personal site! Gives the complete history of the astroid and has lots of pictures, graphs, and even videos!
Graphic
Math2

Math2: Circles

For Students 9th - 10th Standards
This site has many useful formulas and examples relating to circles, including related definitions, circumference of a circle, area of a circle, length of a circular arc, area of a circular sector, equation of a circle in cartesian...
Unknown Type
Khan Academy

Khan Academy: Solve for T

For Students 9th - 10th
In this seven-problem quiz/practice students parameterize rays by solving for t.
Unknown Type
Khan Academy

Khan Academy: Ray Intersection With Line

For Students 9th - 10th
In this seven-question quiz/practice students find where a ray intersects with a line in implicit form.
Website
Other

College of the Redwoods: The Epicycloid

For Students 9th - 10th Standards
This resource gives a brief description and history lesson. Shows you how to use epicycloids.
Website
Other

College of the Redwoods: Nephroid

For Students 9th - 10th Standards
This resource describes what a nephroid is and what it looks like in graph form.
Handout
National Council of Teachers of Mathematics

The Math Forum: Circles

For Students 9th - 10th Standards
Various forms of equations of circles are presented at the Math Forum: center-radius form, general form, diameter form, three-point form, and parametric form.
Activity
Texas Instruments

Texas Instruments: Vectors Vocabulary Quiz

For Teachers 9th - 10th
This can be used as a short vocabulary quiz for vector definitions.
Website
Other

College of the Redwoods: Special Plane Curves

For Students 9th - 10th
This resource gives a report on asteroids including brief history and pictures.
Interactive
University of St. Andrews (UK)

University of St. Andrews: Cissoid of Diocles

For Students 9th - 10th
This site, which is provided for by the University of St. Andrews, describes the properties behind cissoids and graphs them.
Graphic
University of St. Andrews (UK)

University of St. Andrews: Lissajous Curves

For Students 9th - 10th
This site, which is provided for by the University of St. Andrews, allows you to zoom in/out and add evolutes, involutes, etc.
Interactive
University of St. Andrews (UK)

University of St. Andrews: Involute of a Circle

For Students 9th - 10th
This site, which is provided for by the University of St. Andrews, allows you to zoom in/out and add evolutes, involutes, etc.
Interactive
University of St. Andrews (UK)

University of St. Andrews: Conchoid of De Sluze Applet

For Students 9th - 10th
Zoom in and out, and add evolutes, involutes, etc.
Interactive
University of St. Andrews (UK)

University of St. Andrews: Astroid

For Students 9th - 10th
This site from the University of St. Andrews allows you to zoom in/out and add evolutes, involutes, etc.
Graphic
University of St. Andrews (UK)

University of St. Andrews: Epicycloid

For Students 9th - 10th
Very cool site. Allows you to zoom in/out and add evolutes, involutes, etc.
Graphic
Wolfram Research

Wolfram Math World: Folium of Descartes

For Students 9th - 10th
This site gives the parametric, cartesian, and polar equations for this plane curve. Also given is the point of discontinuity, equation for the asymptote, and area under the curve.
Interactive
University of St. Andrews (UK)

University of St. Andrews: Hypocycloid

For Students 9th - 10th
Shows the graph and the parametric cartesian equation. The site also includes links to graphs of related curves and definitions of the associated curves.

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